Abstract.
The formalism of monadic second-order (MS) logic has been very successful in unifying a large number of algorithms for graphs of bounded treewidth. We extend the elegant framework of MS logic from static problems to dynamic problems, in which queries about MS properties of a graph of bounded treewidth are interspersed with updates of vertex and edge labels. This allows us to unify and occasionally strengthen a number of scattered previous results obtained in an ad hoc manner and to enable solutions to a wide range of additional problems to be derived automatically.
As an auxiliary result of independent interest, we dynamize a data structure of Chazelle for answering queries about products of labels along paths in a tree with edges labeled by elements of a semigroup.
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Received February 10, 1997.
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Hagerup, T. Dynamic Algorithms for Graphs of Bounded Treewidth . Algorithmica 27, 292–315 (2000). https://doi.org/10.1007/s004530010021
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DOI: https://doi.org/10.1007/s004530010021